Honestly, being a female in a vain world of fashion and pressure to look a certain way, i think it is fair that you ask your parents and explain to them why you need to set yourself up with a basic set of cosmetics that you could use everyday/often. it doesnt mean you have to slurge. just pick out essential items.
its not practical for them to expect you to save up $20/month to afford what you need. to be honest, i lived off mascara and eyeliner from drugstores as a teenager until i went to university before buying MAC. but all in all, depending on your financial situation, you should start off by telling your parents that you have a need for make up as much as you need tampons. the same as boys need their skateboards or whatever. maybe even ask them for birthday and holiday gift advances and set up a reward system with your grade. i dont know if you've explained any of this to them, but it sounds like you haven't. if they won't let you have a job, then they should be prepared to cover your needs as supporting parents. lol
my bf and i have a pact where if i acheive any As, exams and final grades he'll buy me a gift. its a great system! lol maybe ask your parents about it.